I was looking for this some years ago and had some cpp half ready for when rstan added complex number support, but that never eventuated and code is much cheaper now! Who knows maybe I port it back or use stan math somehow again but for now I got a few things that have been on the wish list for a while - faster performance and compile, laplace approx, hmc initialisation around the mode with auto metric etc… strange times
Edit: sorry yes Lyupanov solve (simplified Sylvester) with complex schur decomp was one of the puzzle pieces